7 people can paint 4 walls in 46 minutes. How many minutes will it take for 9 people to paint 6 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 4\text{ walls}\\ p &= 7\text{ people}\\ t &= 46\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{4}{46 \cdot 7} = \dfrac{2}{161}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 6 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{6}{\dfrac{2}{161} \cdot 9} = \dfrac{6}{\dfrac{18}{161}} = \dfrac{161}{3}\text{ minutes}$ $= 53 \dfrac{2}{3}\text{ minutes}$ Round to the nearest minute: $t = 54\text{ minutes}$